In a data, if $l =40, h=15, f _1=7, f _0=3, f _2=6$, then the mode is
- A$82$
- ✓$62$
- C$52$
- D$72$
Answer: B.
View full solution →Question types
MODEL PAPER 9 (STANDARD) question types
44 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
44
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
8 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
MODEL PAPER 9 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the dice is $7$ is
- A$7$
- B$2$
- ✓$0$
- D$1$
Answer: C.
View full solution →A letter is chosen at random from the letters of the word ASSOCIATION. Find the probability that the chosen letter is a vowel.
- ✓$\frac{6}{11}$
- B$\frac{7}{11}$
- C$\frac{5}{11}$
- D$\frac{3}{11}$
Answer: A.
View full solution →A piece of paper in the shape of a sector of a circle $($see figure $1)$ is rolled up to form a right$-$circular cone $($see figure $2).$ The value of angle $\theta$ is:
- A$\frac{5 \pi}{13}$
- B$\frac{6 \pi}{13}$
- ✓$\frac{10 \pi}{13}$
- D$\frac{9 \pi}{13}$
Answer: C.
View full solution →In a circle of radius $21 \ cm ,$ an arc subtends an angle of $60^{\circ}$ at the centre. The area of the sector formed by the arc is:
- ✓$231 cm^2$
- B$250 cm^2$
- C$220 cm^2$
- D$200 cm^2$
Answer: A.
View full solution →Assertion (A): $a_n-a_{n-1}$ is not independent of $n$ then the given sequence is an AP.
Reason (R): Common difference $d=a_n-a_{n-1}$ is constant or independent of $n$.
Reason (R): Common difference $d=a_n-a_{n-1}$ is constant or independent of $n$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →Assertion (A): In the given figure, a sphere is inscribed in a cylinder. The surface area of the sphere is not equal to the curved surface area of the cylinder.
Reason (R): Surface area of sphere is $4 \pi r ^2$
Reason (R): Surface area of sphere is $4 \pi r ^2$
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →If $\sqrt{2} \sin \theta=1$, find the value of $\sec ^2 \theta-\operatorname{cosec}^2 \theta$.
View full solution →In Figure, a chord $AB$ of a circle of radius $10 \ cm$ subtends a right angle at the centre
Find
$i$. Area of sector $\text{OAPB}$
$ii$. Area of minor segment $\text{APB}. \ ($Use $\pi=3.14)$
View full solution →Find
$i$. Area of sector $\text{OAPB}$
$ii$. Area of minor segment $\text{APB}. \ ($Use $\pi=3.14)$
$\Lambda B C D$ is a flower bed. If $O \Lambda=21 m$ and $OC =14 m$, find the area of the bed.
View full solution →If $x=a \cos ^3 \theta, y=b \sin ^3 \theta$, prove that $\left(\frac{x}{a}\right)^{2 / 3}+\left(\frac{y}{b}\right)^{2 / 3}=1$
View full solution →A quadrilateral $ABCD$ is drawn to the circumference of a circle. Prove that: $AB + CD = AD + BC$
View full solution →If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
If two pipes function simultaneously, a reservoir will be filled in $12$ hours. One pipe fills the reservoir $10$ hours faster than the other. How many hours will the second pipe take to fill the reservoir?
View full solution →The angle of elevation of the top of a tower from a point $A$ on the ground is $30^{\circ}$. On moving a distance of $20$ metre towards the foot of the tower to a point $B$ the angle of elevation increases to $60^{\circ}$. Find the height of the tower and the distance of the tower from the point $A .$
View full solution →Prove that $(\sin A+\operatorname{cosec} A)^2+(\cos A+\sec A)^2=7+\tan ^2 A+\cot ^2 A$.
View full solution →In Figure, $X Y$ and $X^{\prime} Y^{\prime}$ are two parallel tangents to a circle with centre $O$ and another tangent $A B$ with point of contact $C$ intersects $XY$ at $A$ and $X ^{\prime} Y ^{\prime}$ at $B$ . Prove that $\angle A O B=90^{\circ}$.
View full solution →The ratio of incomes of two persons is $11 : 7$ and the ratio of their expenditures is $9 : 5.$ If each of them manages to save $Rs.400$ per month, find their monthly incomes.
View full solution →A hemispherical depression is cut out from one face of a cubical block of side $7 cm$ , such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.
View full solution →In an $A.P.,$ the $n ^{\text {th }}$ term is $\frac{1}{m}$ and the $m ^{\text {th }}$ term is $\frac{1}{n}$. Find $(i) (mn) { }^{\text {th }}$ term, $(ii)$ sum of first $(mn)$ terms.
View full solution →In a cylindrical vessel of radius $10 \ cm ,$ containing some water, $9000$ small spherical balls are dropped which are completely immersed in water which raises the water level. If each spherical ball is of radius $0.5 \ cm ,$ then find the rise in the level of water in the vessel.
View full solution →Find the lengths of the medians of a $\triangle A B C$ having vertices at $A(0,-1), B(2,1)$ and $C(0,3)$.
View full solution →Read the following text carefully and answer the questions that follow:
The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
Suresh places a mirror on level ground to determine the height of a pole $($with traffic light fired on it$)$. He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Suresh's eye level is $1.5 m$ above the ground. The distance of Suresh and the pole from the mirror are $1.8 m$ and $6 m$ respectively.
$i$. Which criterion of similarity is applicable to similar triangles? $(1)$
$ii$. What is the height of the pole? $(1)$
$iii$. If angle of incidence is $i,$ find tan i. $(2)$
OR
Now Suresh move behind such that distance between pole and Suresh is $13$ meters.He place mirror between
him and pole to see the reflection of light in right position. What is the distance between mirror and Suresh? $(2)$
View full solution →The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
Suresh places a mirror on level ground to determine the height of a pole $($with traffic light fired on it$)$. He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Suresh's eye level is $1.5 m$ above the ground. The distance of Suresh and the pole from the mirror are $1.8 m$ and $6 m$ respectively.
$i$. Which criterion of similarity is applicable to similar triangles? $(1)$
$ii$. What is the height of the pole? $(1)$
$iii$. If angle of incidence is $i,$ find tan i. $(2)$
OR
Now Suresh move behind such that distance between pole and Suresh is $13$ meters.He place mirror between
him and pole to see the reflection of light in right position. What is the distance between mirror and Suresh? $(2)$
Read the following text carefully and answer the questions that follow:
Under the physical and health education a medical check up program was conducted in a Vidyalaya to improve the health and fitness conditions of the students. Reading of the heights of $50$ students was obtained as given in the table below $:$
$i.$ Find the lower class limit of the modal class. $(1)$
$ii.$ Find the median class. $(1)$
$iii.$ Find the assumed mean of the data. $(2)$
$OR$
Find the median of the given data. $(2)$
View full solution →Under the physical and health education a medical check up program was conducted in a Vidyalaya to improve the health and fitness conditions of the students. Reading of the heights of $50$ students was obtained as given in the table below $:$
| $\text{Height (in cm)}$ | $\text{Number of students}$ |
| $135-140$ | $2$ |
| $140-145$ | $8$ |
| $145-150$ | $10$ |
| $150-155$ | $15$ |
| $155-160$ | $6$ |
| $160-165$ | $5$ |
| $165-170$ | $4$ |
$ii.$ Find the median class. $(1)$
$iii.$ Find the assumed mean of the data. $(2)$
$OR$
Find the median of the given data. $(2)$
Read the following text carefully and answer the questions that follow:
An object which is thrown or projected into the air, subject to only the acceleration of gravity is called a projectile, and its path is called its trajectory. This curved path was shown by Galileo to be a parabola. Parabola is represented by a polynomial. If the polynomial to represent the distance covered is, $p(t)=-5 t^2+40 t+1.2$
i. What is the degree of the polynomial $p(t)=-5 t^2+40 t+1.2$ ? (1)
ii. What is the height of the projectile at the time of 4 seconds after it is launched? (1)
iii. What is the name of the polynomial $p(t)=-5 t^2+40 t+1.2$ that is classified based on its degree? (2)
OR
What are the factors of the given quadratic equation $p(x)=x^2-5 x+6$ ? (2)
View full solution →An object which is thrown or projected into the air, subject to only the acceleration of gravity is called a projectile, and its path is called its trajectory. This curved path was shown by Galileo to be a parabola. Parabola is represented by a polynomial. If the polynomial to represent the distance covered is, $p(t)=-5 t^2+40 t+1.2$
i. What is the degree of the polynomial $p(t)=-5 t^2+40 t+1.2$ ? (1)
ii. What is the height of the projectile at the time of 4 seconds after it is launched? (1)
iii. What is the name of the polynomial $p(t)=-5 t^2+40 t+1.2$ that is classified based on its degree? (2)
OR
What are the factors of the given quadratic equation $p(x)=x^2-5 x+6$ ? (2)
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